"if a - 7 = b(x + 2), then x = ? " i need a step by step explanation too.

choice (3), x = (2b+7)/(a-b)

Explanation:

The idea is to get all the x terms to one side (after distributing), then factoring out the common term x, finally divide both sides by (a-b) as shown below

ax-7 = b(x+2)

ax-7 = bx+2b distribute

ax-7+7 = bx+2b+7 ... add 7 to both sides

ax = bx+2b+7

ax-bx = bx+2b+7-bx ... subtract bx from both sides

ax-bx = 2b+7

(a-b)x = 2b+7 factor out the GCF x

x = (2b+7)/(a-b) ... divide both sides by (a-b)

We have all of "2b+7" over "a-b" as one big fraction. This is what choice (3) is showing.

- 2 + 10x³ - 21x² + 19x - 4

step-by-step explanation:

each term in the second factor is multiplied by each term in the first factor

x²(- 2x² + 4x - 1) - 3x(- 2x² + 4x - 1) + 4(- 2x² + 4x - 1) ← distribute

= - 2 + 4x³ - x² + 6x³ - 12x² + 3x -8x² + 16x - 4

collect like terms

= - 2 + 10x³ - 21x² + 19x - 4 ← in standard form